msdb holds Agent jobs. master holds logons, linked servers and system settings (and master database keys used to encrypt certificates), and model is the template database used when any new databases are created on the instance. I highly recommend restoring all of these databases.
https://www.sqlskills.com/blogs/jonathan/downgrading-sql-server-editions/ could help - this is a guide for reinstalling SQL Server to a lower SKU, which I used a couple of weeks back - it's similar to your situation in that you're restoring/recovering a SQL instance over a fresh install.
In it, Jonathan instructs to bring the fresh SQL Server version up to the exact same patch version as it was previously (you can get this from the first row of the ERRORLOG file in the \Log folder of the SQL Server installation if you still have access to the folder from before the issue), then stop the SQL Server service, and replace the data and log files as you've described.
As in the comments on that post, you'd want to make sure the SQL Service is running under the same user account as previously, and your reinstall is to the same directories. You want to restore all of the .MDF/.NDF and .LDF files to the same location they were previously, not just the master.mdf.
Best practice... err.. best practice might be to log a $500 support request with Microsoft.
Best of luck and seasons greetings,